Jack and Jill are maneuvering a 3300 kg boat near a dock. Initially the boat\'s

Question

Jack and Jill are maneuvering a 3300 kg boat near a dock. Initially the boat's position is (3, 0, 4.5)m and its speed is 1.4 m/s. As the boat moves to position (4, 0, 4.5) m, Jack exerts a force ( -360, 0, 200) N and Jill exerts a force (110, 0, 390) N.

a) How much work does Jack do?

b) How much work does Jill do?

c) What is the angle between the force that Jill exerts and the average velocity of the boat?

d) Assuming that we can neglect the work done by the water on the boat, what is the final speed of the boat?

Please show all work. Round to 4 decimal places if possible.

Explanation / Answer

a) We will apply the Energy Principle. System: the boat. Surroundings: Jack and Jill interacting with the boat. In general, the Energy Principle states that Esys = W = F.r where the last equality holds for a constant force acting over the distance r . In what follows

r = rf ri = (4, 0, 4.5) - (3, 0, 4.5) = (1, 0, 0) m

The amount of work done by Jack is:

FJack .r = ( -360, 0, 200) N* (1, 0, 0) m = -360 N.m

b) The amount of work done by Jill is:

FJill .r = (110, 0, 390) N* (1, 0, 0) m = 110 N.m

d) Applying the Energy Principle:

Esys = KE = 0.5*M(vf^2 - vi^2) = Fnet.r = -250 J

0.5*3300*(vf^2 - 1.4^2) = -250

vf = 1.345 m/s

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